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m1 sees that the server_id of the INSERT is 23 which is not the same as m1's server_id (1)

m1 executes INSERT

OK, all well and good. But, why doesn't s3 get to receive anything? Because log_slave_updates is not enabled, m1 does not save the INSERT and the original server_id posting the INSERT into its own binary logs.

If log_slave_updates was enabled on m1, now follow along your example and let's see what should happen: